Strengthening the No-Go Theorem for QRNGs

Quantum random numbers are essential for security against quantum algorithms. Randomness as a beacon is a service being provided for companies and governments to upgrade their security standards from RSA to PQC-QKD or PQC-RSA protocols. Both security mechanisms assume trust in the service provider unless one aims for device-independent protocols. How does an entity ensure that the beacon service has a quantum signature other than relying on faith? Specifically, given a bit-stream, can a user verify a quantum signature in it? Researchers claim this is indecipherable and have stated a no-go theorem for post-processed bit-streams [Physical Review A \textbf{109}, 022243 (2024)]. In this article, we corroborate the results of the no-go theorem while discussing its nuances using two different random number generators and four test methods. These include the NIST statistical test suite and machine learning algorithms that strengthen the theorem. This work is relevant for companies and governments using QRNG, provided to enhance security against quantum threats.